As you want to do Master of Business Administration (MBA) course in United Kingdom (UK) and asked for top colleges for it, I am mentioning them, check below for the details

King's College London
University of Oxford - Saïd Business School
Heriot-Watt University - Edinburgh Business School (EBS)
LSE - The London School of Economics and Political Science
Imperial College Business School
London Business School (LBS)
Cranfield School of Management
Manchester Business School (MBS), The University of Manchester
University of Dublin - Trinity College
Warwick Business School (WBS), University of Warwick
University of Edinburgh Business School (UEBS)
Aberdeen Business School
University of Birmingham - Birmingham Business School
Cass Business School, City University London
University of Westminster - Westminster Business School
Durham University Business School
University of Cambridge - Judge Business School
University College Dublin (UCD) - Michael Smurfit School of Business
Hult International Business School - Europe Campus (London)
Bradford University School of Management
University of Strathclyde - Strathclyde Business School
Griffith College Dublin
Dublin City University Business School
Brunel Business School
Cardiff Metropolitan University (UWIC) - Cardiff School of Management
London Metropolitan University
Loughborough University
Lancaster University Management School (LUMS)
Middlesex University Business School
The University of Northampton - Northampton Business School
University of Essex - Essex Business School
University of Exeter Business School
Henley Business School
Nottingham University Business School
University College Cork
Edinburgh Napier University
Cardiff Business School - Cardiff University